Math Chapter Wise

EnglishPGT 2004

Q221.If y = sin px and yn is the nth derivative of the function, then the value of 4 1 2 5 y y will be

Ap4 B-p4 Cp6 D-p6

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EnglishPGT 2004

Q222.1 1 1 1 lim... 1 2 2 x n n n n n →∞ + + + + + + + + + + + + + + + + + + + + + + + + + + + + is equal to

Alog2 Blog3 Clog 4 Dnone of these

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EnglishPGT 2003

Q223./4 1 tan lim 1 2sin x π → − = − is equal

A0 B1 C–1 D2

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EnglishPGT 2003

Q224.1 sin lim x →∞+ is equal to

A0 B–1 C1 DNone of these

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EnglishPGT 2003

Q225.If f''(x) is continuous at x=a, then 2 0 () 2 () () lim h f a h f a f a h h → + − + − + − + − + − + − + − + −

A'( )/f a B''( )/f a C0 D∞

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EnglishPGT 2003

Q226.log 1 lim x e x x e → − is equal to

Ae Be–1 Ce2 De–2

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EnglishPGT 2002

Q227.If 2 x x 0 0 1 t dt lim 1 x sinx a t → = − − + + ∫ ∫, then the value of a is:

A2 B3 C4 D5

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EnglishPGT 2002

Q228.If (((()))) 2 f(x) log x 1 = + = + then x 2 f(x) f(2) lim x 2 → − is equal to:

A0 B4/5 C1/2 D5/4

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EnglishPGT 2002

Q229.If 1 forx 0 f(x) 1 x forx 0 ≤ = + > then 2 f(x)dx − ∫ ∫ is equal to:

A0 B6 C8 D10

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EnglishPGT 2002

Q230.Let (((()))) 2 sin x f(x): x 0,f(0) 0 x = ≠ = ≠ = ≠ = ≠ =. then f (x) is:

AContinuous and derivable at x = 0 Bdiscontinuous at x = 0 CCon. but not differentiable at x = 0 DNone of these

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EnglishPGT 2002

Q231.Let (()) 3 x 1 acosx bsinx f(x),x 0,f(0) 1 x + − = ≠ = ≠ = ≠ = ≠ = if f(x) is continuous at x=0, a and b are given by:

A5 3, 2 2 B–5,–3 C5 3, 2 2 − − DNone of these

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EnglishPGT 2002

Q232.Let ((()) { { } } f(x) x x x 1, = − + = − + = − + = − + then f is:

Acontinuous but not differentiable at x= 0 Bdiscontinuous at x = 0 Ccontinuous and differentiable both at x= 0 DNone of these

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EnglishPGT 2002

Q233.Let f(x) be defined by: sin2x:0 x 6 f(x) ax b: x 1 6 π < ≤ = π + < ≤ + < ≤ + < ≤ + < ≤ The value of a and b such that f and f' are continuous, are:

A3 a 1,b 2 6 π = − B3 1 a,b 2 2 = C3 1 a,b 2 2 6 π = + DNone of these

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EnglishPGT 2002

Q234.If (((()))) (((()))) ((()) 2 2 1 x 1 y a x y, − + − = − − + − = − − + − = − − + − = − then dy? dx =

A2 1 x 1 y − B2 1 y 1 x − C2 1 x 1 y − DNone of these

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EnglishPGT 2002

Q235.If (((()))) 2 f(x) 9 x, = − = − then x 2 f(2) f(x) lim x 2 → − is:

A2/5 B−2/5 C0 DNone of these

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EnglishPGT 2000

Q236.The value of 1 x x 1 limx − → is given by:

A1 B0 Ce D1/e

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EnglishPGT 2000

Q237.The value of 1 x x 0 tanx lim x → is equal to:

A1 B0 Ce DNone of these

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EnglishPGT 2000

Q238.If 1 x t t = + = + and 1 y t t = − = − then 2 d y dx is equal to:

A2 2 4t(t 1) − − B3 2 3 4t (t 1)− − − C2 2 4t(t 1) − − D2 2 1 (t 1)(t 1)− + −

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EnglishPGT 2000

Q239.For differentiability of a function, continuity is:

ASufficient BNecessary CSufficient and Necessary DNone of these

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EnglishRajasthan TGT 2016

Q240.If x 0 x 0 limkxcotx limxcotkx, → → = then value of k is to

Aonly 1 Bonly –1 C±1 D±1/2

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